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Onion is sold for $5$ consecutive months at the rate of $\text{Rs}\; 10, 20, 25, 25,$ and $50 \; \text{per kg},$ respectively. A family spends a fixed amount of money on onion for each of the first three months, and then spends half that amount on onion for each of the next two months. The average expense for onion, $\text{in rupees per kg},$ for the family over these $5 \; \text{months}$ is closest to

1. $18$
2. $16$
3. $26$
4. $20$

Let's draw the table for $5$ months:

$\begin{array}{|l||c|c|c|c|c|} \hline & 1^{\text{st}}\;\text{month} & 2^{\text{nd}}\;\text{month} & 3^{\text{rd}}\;\text{month} & 4^{\text{th}}\;\text{month} & 5^{\text{th}}\;\text{month} \\\hline \text{Onion sold} & ₹\;10 & ₹\;20 & ₹\;25 & ₹\;25 & ₹\;50 \\ \text{(Rs./kg)} & & & & & \\\hline \text{Amount spend} & ₹\;100 & ₹100 & ₹\;100 & ₹\;50 & ₹\;50 \\ \text{by family} & & & & & \\\hline \text{Weight} & 10\;\text{kg} & 5\;\text{kg} & 4\;\text{kg} & 2\;\text{kg} & 1\;\text{kg} \\\hline \end{array}$

Total amount spent by family $=₹\;400$

Total onion weight $=22\; \text{kg}$

$\therefore$ The average expense for onion, in rupees per kg, for the family over these $5$ months $= \dfrac{₹\;400}{22\;\text{kg}}$

$\qquad \qquad = \frac{200}{11} = 18.18 \cong 18\;\text{rupees/kg}.$

Correct Answer $:\text{A}$
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